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Academy of Economic Studies Doctoral School of Finance and Banking - DOFIN

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REVIEW OF PREVIOUS RESEARCH

Cointegration analysis, regarded as perhaps the most revolutionary development in econometrics since mid’80s, used by (Granger, 1986; Engle and Granger, 1987; Johansen, 1988; Johansen and Juselius, 1990)

VOLATILITY MODELS

GARCH

TGARCH:

EGARCH:

COMPONENT GARCH MODEL

The conditional variance in the GARCH(1,1) model can

be written as:

=>

Allowing for the possibility that σ2 is not constant over time, but a time-varying trend qt, yields:

Dt is a slope dummy variable that takes the value Dt = 1 for εt < 0 and Dt = 0 otherwise, in order to capture any asymmetric responses of volatility to shocks.

DATA

FIRST 2200 observations for each stock market index were used for modeling

LAST 125 were kept out of sample to be used for forecasting volatility

Returns were computed using the prices log difference:

DATA STATISTICS FOR BET SERIES

BET Index the main indicator on the progression of Bucharest Stock Exchange, is a free float weighted capitalization index of the most liquid 10 companies listed on the BSE regulated market. It was launched in September 19, 1997, when its value stood at 1,000 points.

DATA STATISTICS FOR DAX SERIES

DAX Index, is the most commonly cited benchmark for measuring the returns posted by stocks on the Frankfurt Stock Exchange. Started in 1984 with a value of 1000, the index is comprised of the 30 largest and most liquid issues traded on the exchange.

DATA STATISTICS FOR WIG20 SERIES

WIG20 Index, the main index of Warsaw Stock Exchange is calculated based on a portfolio comprised of shares in the 20 largest and most traded companies.. The index base date is April 16, 1994; and its base value is 1, 000 points.

CONDITIONAL VOLATILITY FOR GARCH MODELS

BET Index

CONDITIONAL VOLATILITY FOR GARCH MODELS

DAX Index

CONDITIONAL VOLATILITY FOR GARCH MODELS

WIG20

CGARCH Components Chart

BET Index

CGARCH Components Chart

DAX Index

CGARCH Components Chart

WIG20 Index

FORECASTING VOLATILITY

I used out-of-sample data in order to forecast volatility by using the last 125 observations

GARCH models are measured by the coefficient of determinations R2 coming from regressing squared returns on the volatility forecast: